Geometrothermodynamics for Black holes and de Sitter Space

In this report, a general method to extract thermodynamic quantities from solutions of the Einstein equation is developed. In 1994, Wald established that the entropy of a black hole could be identified as a Noether charge associated with a Killing vector of a global space-time (pseudo-Riemann) manifold. We reconstruct Wald's method using geometrical language, e.g$.$, via differential forms defined on the local space-time (Minkowski) manifold. Concurrently, the abstract thermodynamics are also reconstructed using geometrical terminology, which is parallel to general relativity. The correspondence between the thermodynamics and general relativity can be seen clearly by comparing the two expressions. This comparison requires a modification of Wald's method. The new method is applied to Schwarzschild, Kerr, and Kerr--Newman black holes and de Sitter space. The results are consistent with previous results obtained using various independent methods. This strongly supports the validity of the area theorem for black holes.Comment: 14 page

Model study of the sign problem in a mean-field approximation

We study the sign problem of the fermion determinant at nonzero baryon chemical potential. For this purpose we apply a simple model derived from Quantum Chromodynamics, in the limit of large chemical potential and mass. For SU(2) color, there is no sign problem and the mean-field approximation is similar to data from the lattice. For SU(3) color the sign problem is unavoidable, even in a mean-field approximation. We apply a phase-reweighting method, combined with the mean-field approximation, to estimate thermodynamic quantities. We also investigate the mean-field free energy using a saddle-point approximation.Comment: 7 pages, 2 figures, talk presented at the XXV International Symposium on Lattice Field Theory, July 30 - August 4, 2007, Regensburg, German

Quantum effects of black holes and the cosmological constant problem

A quantum equation of gravity is proposed using geometric quantization of general relativity. Quantum equation for a black hole is solved using the Wentzel-Kramers-Brillouin (WKB) method. Quantum effects of a Schwarzschild black hole are provided by solving a quantum equation of gravity requiring a stationary phase and also using the Einstein-Brillouin-Keller (EBK) quantization condition, and they are consistent each other. WKB method is also applied to the McVittie-Thakurta metric, which is describing a system consists of Schwarzschild black holes and a scalar field. A possible interplay between quantum black holes and scalar field are investigated in detail. A number density of black holes in the universe is obtained using statistical mechanics on a system consisting of black holes and a scalar filed. A possible solution for the cosmological constant problem is proposed in basis of a statistical consideration.Comment: 13 pages, 1 figur

Asymptotic Efficiency of the OLS Estimator with Singular Limiting Sample Moment Matrices

This paper presents a time series model that has an asymptotically efficient ordinary least squares (OLS) estimator, irrespective of the singularity of its limiting sample moment matrices. In the literature on stationary time series analysis, Grenander and Rosenblatt's (1957) (G-R) classical result is used to judge the asymptotic efficiency of regression coefficients on deterministic regressors satisfying Grenander's condition. Without this condition, however, it is not obvious that the model is efficient. In this paper, we introduce such a model by proving the efficiency of the model with a slowly varying (SV) regressor under the same condition on error terms constrained in G-R. This kind of regressor is known to display asymptotic singularity in the sample moment matrices, as in Phillips (2007), such that Grenander's condition fails.

Consistent simulation of non-resonant diphoton production at hadron collisions with a custom-made parton shower

We have developed a Monte Carlo event generator for non-resonant diphoton ($\gamma\gamma$) production at hadron collisions in the framework of GR@PPA, which consistently includes additional one-jet production. The jet-matching method developed for initial-state jet production has been extended to the final state in order to regularize the final-state QED divergence in the $qg \rightarrow \gamma\gamma + q$ process. A QCD/QED-mixed parton shower (PS) has been developed to complete the matching. The PS has the capability of enforcing hard-photon radiation, and small-$Q^{2}$ photon radiations that are not covered by the PS are supplemented by using a fragmentation function. The generated events can be passed to general-purpose event generators in order to perform the simulations down to the hadron level. Thus, we can simulate the isolation requirements that must be applied in experiments at the hadron level. The simulation results are in reasonable agreement with the predictions from RESBOS and DIPHOX. The simulated hadron-level events can be further fed to detector simulations in order to investigate the detailed performance of experiments.Comment: 23 pages, 15 figure